I also agree with what kml is saying in the first couple paragraphs.
What your X did (taking S2 overnight w/o your consent) was wrong. I was frustrated with my X's control of the kids the past year, but I never would have taken that step. I think you are absolutely doing the right thing to make a reasonable offer of a step-up plan, largely because it will contain all the extra language that makes things legally enforceable. The courts want both parents to play an active role in childrens' lives -- of course while being very seriously concerned about the child's well-being and the fitness of the parents.
What I have to say next is more speaking in generalities, and not specifically about your situation. In these high-conflict custody situations, both sides start vilifying the other person. War ensues, L's get paid a lot of money, the kids and parents suffer emotionally and financially, and, in the end, you end up with a custody plan similar to what you are offering right now anyways, for instance.
In my (completely different from your) situation, I felt like my X was withholding access, coaching the children, in it for the money, using double standards, etc. I think she was not comfortable with me having more access to the kids, or she wanted extra control over the process that was not reasonable. I felt that every step of the way I was doing my best to de-escalate the situation while simultaneously asserting what I thought was a reasonable solution. It didn't really work in my situation... we didn't go all the way to the expensive trial but we got really really close.
I can see you are really hurt. Your X is driving around with OW, parading her in front of your face, taking S2 overnight and lying about the reasons. I would be irate. I don't think it matters if he has a personality disorder or is just upset about the D -- he is very very difficult to work with right now. He is tossing bait around and hoping you bite so you are drawn into conflict. The conflict feeds his impression of you, it helps justify what he is doing, he thrives on viewing you as controlling, then he can justify his actions to himself without any guilt.
I guess what I'm suggesting is that you focus on minimizing the conflict and keep it business-like. You are clearly a strong and emotionally aware person and the more mature parent by leaps and bounds. But I see that, at times, your X baits you into little arguments and tiffs. As much as your blood boils, he's not listening to what you say back to him anyways, and he's just using it to further the conflict. I don't view it as being the bigger person and walking away, it's about focusing on the end game -- getting to a strictly business co-parenting relationship while minimizing the emotional energy, money, and time you have to burn to get there.
I'm not suggesting he's off the hook or anything. Control what you can and try to ignore the bait (if you can) or use your L as needed.
Your X is looking for fuel to stoke his fire to justify his actions. Starve him of his fuel supply (the best you can).
Hang in there. You are a strong parent and you'll get through this.
